Most of the flour used in the West today is made from wheat
In the UK (not in other countries) there are regulations for bread made from wheat flour called wholemeal or whole germ (but not for brown or any other label)
Wholemeal - all the flour used as an ingredient in the preparation of the bread must be wholemeal. The term "wholemeal" is not defined in law, however it is generally accepted that wholemeal flour is the entire wheat grain, which contains the bran and the germ.
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Wheat germ – the bread must have an added processed wheat germ content of at least 10% calculated on the dry matter of the bread.
So wholemeal bread contains all the grain (ie including the outer bran and the germ)
However modern methods enable grains to be extremely finely milled nowadays so the particles are tiny. This means that although wholemeal bread contains higher quantities of nutrients than white bread it is often quite high on the glycemic index and they will be processed quickly causing the glucose to rise quickly.
If you are eating any bread then it is probably far better to look for those made with heavier, coarser ground flours (many rye breads are like this) or breads where many whole seeds and grains are visible.
This picture from a lecture by Prof Jim Mann shows quite clearly what I mean (red marks mine!)
Of course there are grains other than wheat and all grains can be eaten without being ground or refined at all , personally that's what I think whole grains should mean (scroll to about a quarter way down for pictures and explanations of the various grains)
http://www.seriouseats.com/2014/03/...cient-grains-gluten-free-types-of-grains.html
I'm not T2 but I do know that there are some type 2s on here that use some whole grains such as whole grain barley and brown rice as part of their diets.